Perpetual American vanilla option pricing under single regime change risk. An exhaustive study

TL;DR

This paper thoroughly analyzes the pricing of perpetual American vanilla options considering the risk of a single regime change in volatility and dividends, revealing a phase transition-like behavior in the pricing equation.

Contribution

It introduces a novel framework for modeling regime change risk in perpetual American options, connecting financial modeling with physical phase transition concepts.

Findings

Pricing equation depends on regime change probability

Identifies phase transition behavior in option prices

Provides analytical results aligning with market observations

Abstract

Perpetual American options are financial instruments that can be readily exercised and do not mature. In this paper we study in detail the problem of pricing this kind of derivatives, for the most popular flavour, within a framework in which some of the properties |volatility and dividend policy| of the underlying stock can change at a random instant of time, but in such a way that we can forecast their final values. Under this assumption we can model actual market conditions because most relevant facts usually entail sharp predictable consequences. The effect of this potential risk on perpetual American vanilla options is remarkable: the very equation that will determine the fair price depends on the solution to be found. Sound results are found under the optics both of finance and physics. In particular, a parallelism among the overall outcome of this problem and a phase transition is established.